English

The lexicographic degree of the first two-bridge knots

Geometric Topology 2018-09-14 v2 Algebraic Geometry

Abstract

We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree of a lexicographic parametrisation of such a knot. This allows us to transform this problem into a study of real algebraic trigonal plane curves, and in particular to use the braid theoretical method developed by Orevkov.

Keywords

Cite

@article{arxiv.1501.06393,
  title  = {The lexicographic degree of the first two-bridge knots},
  author = {Erwan Brugallé and Pierre-Vincent Koseleff and Daniel Pecker},
  journal= {arXiv preprint arXiv:1501.06393},
  year   = {2018}
}

Comments

30 p., 58 fig., 6 tables